Helmholtz equation
Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains
... Remark Note that in the stretched coordinate system , ϑ, the original domain A is trans- formed into the circular annulus of radii a and b, respectively. Hence, in this system one can use classical techniques, including ...
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Solving Helmholtz Equation by Meshless Radial Basis Functions Method
... The scattered data interpolation with radial basis functions (RBFs) which was first proposed by Kansa [13] in 1990 are powerful tools in multi-variable approximation. It has been successfully used to solve various ...
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Shape Representation Using the Helmholtz Equation
... In Chapter IV, we extend it to consider Brownian motion that originates outside the shape. To prevent this Brownian motion from continuing infinitely, we introduce an exponential dying time for the particle. This dying ...
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High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities.
... We have shown in this chapter how to apply the method of difference potentials when computing singular solutions of the Helmholtz equation while preserving high-order accuracy. The key idea is to regularize ...
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2. A new method for solving the modified Helmholtz equation
... Abstract. In this paper, the Cauchy problem for the modified Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based ...
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Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell
... In this contribution, a suitable methodology, based on the theory of spherical harmonics [17], has been devel- oped in order to compute the solution of the Robin prob- lem for the Helmholtz equation in ...
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The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges
... the Helmholtz equation in an exterior multiply connected domain bounded by closed curves is considered in monographs on mathematical physics, for instance, in ...this equation in the exterior of ...
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High Order Finite Difference Method for Helmholtz Equation in Polar Coordinates
... In polar coordinates, the symmetric problem can be described more concisely. A finite difference method was proposed to solve the parabolic equation in polar coordinates in [10]. Britt et al. [11] constructed a ...
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High-frequency asymptotics for the modified Helmholtz equation in a half-plane
... Based on the integral representations of the solution derived via Fokas’ transform method, the high-frequency asymptotics for the solution of the modified Helmholtz equation, in a half-plane and subject to ...
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The parallelization of helmholtz equation related to breast cancer growth
... on Helmholtz equation concept, corollary and discretization using finite difference method with three points central difference ...multi-dimensional Helmholtz equations under consideration in solving ...
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Some properties and applications of the Teodorescu operator associated to the Helmholtz equation
... the Helmholtz equation is an elliptic partial differential equation describing the electromagnetic wave, which has important applications in geophysics, medicine, engineering application, and many ...
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Modeling Of The Gaussian Laser Beam By Approximate Solution Of Helmholtz Equation
... Lasers are devices that amplify or increase the intensity of light to produce a highly directional, high-intensity beam that typically has a very pure frequency or wavelength. The beams come in sizes ranging from ...
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A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation
... We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at x 1 and the solution is sought in the interval 0 < x < 1. A spectral method together with choice of ...
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Landweber iterative regularization method for identifying the unknown source of the modified Helmholtz equation
... on the modified Helmholtz equation. In [, ], the authors used the quasi-reversibility method to identify the unknown source of the modified Helmholtz equation on half strip region and half ...
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Bistable dark solitons of a cubic quintic Helmholtz equation
... We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an ...
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Finite Difference Solution of the Helmholtz Equation Based on Two Domain Decomposition Algorithms
... wave equation is an important problem. The Helmholtz equation is the ver- sion of acoustic wave equation in the frequency ...the Helmholtz equation have been under ac- tive ...
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A Fast High Order Algorithm for 3D Helmholtz Equation with Dirichlet Boundary
... In this paper, our aim is to discretize the Helmholtz equation with fourth-order finite difference method and build a fast algorithm using the discrete Fourier-sine transformation. On the other hand, the ...
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Iterative three dimensional Helmholtz Equation solutions using the Wave Expansion Method
... the Helmholtz equation impose restrictions on the coarse grid, requiring th a t these grids be sufficiently fine for the algorithm to be ...the Helmholtz operator on very coarse meshes, since such ...
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A New Parabolic Approximation to the Helmholtz Equation
... These preliminary numerical results show that the parabolic approximation investigated here captures the correct full wave behavior of the Helmholtz equation for the targets and boundary[r] ...
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Two-level preconditioners for the Helmholtz equation
... I. G. Graham, E. A. Spence, and E. Vainikko. Recent Results on Domain Decomposition Preconditioning for the High-Frequency Helmholtz Equation Using Absorption, pages 3–26. Geosystems Mathematics. Springer, ...
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